Things were going well.
Orbital colonies, Moon bases, a mission to Mars, solar power satellites, clean fusion, the whole nine yards.
Geopolitically, things were better than they’d been in decades.
Medically, going great.
Socially, …, well, it was calm enough.

Then the Fucking Comet came through, spewing radiation everywhere.

Mars, then the Orbitals & the Moon got weird before the Powers That Be cut communications. Claimed that the Fucking Comet was messing with the signal, but couldn’t explain what we saw before that signal cut. The sicknesses. The fighting. The eating. And the slurred warnings about bodies.

Of course, once the Dead Rose here on Earth, we pretty much figured it out.

Fighting the Dead is a problem that only gets worse over time, and while we didn’t lose, it became pretty obvious that we weren’t going to be winning in the long term. Cities fragmented into townships, towns into villages, and the whole damn world divided up into what you could defend, surrounded by what you couldn’t.

Well, for most of us. For the Powers That Be, there were laser-launched military ships to clear out orbital colonies, “to act as secure coordination points”.
There were transports “to secure vital resources”.
Over time, despite the rhetoric, it became clear that the plan was, in fact, “We will take all of the resources we can and go into orbit above this Dead-choked World, and then we’ll send for you. Or not.”, and there was nothing anyone could do.

At least until that guy staggered into a dive bar in a no-name township on the Gulf Coast, asked for the folks who’d dealt with the last big Dead incursion, bought us a round of piss-weak beer, and asked if we’d be interested in going to Space.

His story sounded stupid at first; De-mothballing an old Single Stage To Orbit machine, re-taking an Orbital Manufacturing plant, and ferrying people up to it. No idea what the Dead on the thing were like, but they had telemetry, and it had seemed workable.

That is, up until they found that the heat tiles were shot. No landings possible with that thing. No staged missions to bring the station back section by section, just a one-shot mission with everyone on board, and a team ready to get the reactor running, the station spun up, and the life support on line before everyone ran out of air.

They had the skills for that part. What they didn’t have were the folks to keep them alive long enough to do it, and that’s where he was hoping we’d come in, …

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There are a few different ways this one could be done;

Great Big Heroes

The characters really are sufficiently bad-ass that the prospect of moving through an orbital habitat filled with Zombies, while protecting the teams trying to bring it back to life & stopping the zombies from getting into the spacecraft, all with a ticking countdown running and no escape plan? … Not that far-fetched.

System-wise, I was thinking of Wushu for this one; It’s less about how you kill zombie #47, and more about how awesomely you did it.

This would probably be the one or two session highly descriptive & cinematic version of the game.

Wushu is a roleplaying game where groups of friends sit safely on their asses and tell each other a shared story of high-flying, hyper-stylized action. The emphasis is always on entertainment; this isn't a game where smart tactics and careful resource management lead to clearly-defined victories. It's more like improv theater or a radio play or a drunken bullshit session. The only way to win is to make sure everyone has a good time.
There's a free version of the rules here - http://danielbayn.com/wushu/

Sneaky Rat Bastards

Only idiots try to take on a zombie hoard, or indeed a scavenger caravan, head-on.
Dead idiots.
People who want to live use rat-bastard cunning.

This would be the longer version, where the characters are not getting into stand-up fights with zombies, and are instead scuttling around in the vents & attracting as little attention as possible while they get enough of the station just livable enough to act as a base of operations, then expand out from there.

Fate Accelerated Edition would seem like a good fit.

Fate Accelerated Edition is a simple system, focused on the how of things, rather than on specific skills; Yes, your character is an experienced badass, but do they clear that room by being Forceful, Sneaky, Clever, ... ?
Works very well in circumstances where you want to set yourself/your team up for success later, even if it's bad for you right now, which means that it lends itself to making non-badass characters actually fun to play.
FAE is freely available here; https://fate-srd.com/fate-accelerated/get-started

Dumb Luck

The comedy approach.
The characters defeated the great big zombie hoard by dumb luck & a flash-flood / tornado which carried away the bulk of the zombies, and have been drinking on an edited version of the story ever since.
They signed on to this because anything has to be better than that shitty no-name town, right? … Right?

They’re a bit crap, but if they can just fluke their way through this, maybe they’ll become the heroes they want to be.
Or at least maybe they’ll be allowed to stay.